Question: The grades on a chemistry midterm at Loyola are normally distributed with $\mu = 69$ and $\sigma = 4.0$. Luis earned a $62$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{62 - {69}}{{4.0}}} $ ${ z \approx -1.75}$ The z-score is $-1.75$. In other words, Luis's score was $1.75$ standard deviations below the mean.